Chapter 3 of 6 · 11 min

The entry price

Why one turn of purchase price moves returns more than almost anything else, and the most you can pay.

By the end of this chapter you can

Calculate MOIC and IRR at a given price
Show what one turn cheaper does to the IRR
Work out the highest entry multiple for a target IRR
Back out the price paid from a reported multiple of money

The intuition

Two people buy identical houses on the same street with the same mortgage and sell them on the same day for the same price. One paid $20,000 more at the start. The bank lent them both the same amount, so the extra $20,000 came out of her own savings, and her profit is $20,000 smaller on a bigger deposit.

Buyouts work the same way. Lenders size the debt off cash flow, not price, so every extra turn the sponsor pays is funded entirely with equity, while the exit is exactly the same.

The key idea

Paying more changes only the equity check. The exit equity is the same, so MOIC and IRR fall. Turned around: exit equity ÷ target MOIC is the most equity you can put in, which sets the most you can pay.

Why it works

Debt = turns × EBITDA. The lenders look at the cash flow the business can service. The price does not enter into it.
Entry equity = EBITDA × (entry multiple − turns of debt). One more turn of price is one more turn of EBITDA in equity.
Exit equity does not depend on the price. Exit EBITDA, the exit multiple and the debt left are all set by the plan.
The effect grows with leverage. At 5.0x of debt on a 10x price, one turn is a fifth of the check; at 6.0x it is a quarter.
The most you can pay = (exit equity ÷ target MOIC + debt) ÷ EBITDA. A target IRR becomes a target MOIC first: (1 + IRR)^n.
The winner's curse. In an auction the winner is whoever paid most, and unless their plan was also the best, the extra price came straight out of their return.

EBITDA $100M, 5.0x of debt, and a plan that gives $1,200M of exit equity in five years

At 9x: equity 900 − 500 = 400	3.0x, 24.6%
At 10x: equity 1,000 − 500 = 500	2.4x, 19.1%
At 11x: equity 1,100 − 500 = 600	2.0x, 14.9%
Target 20% IRR over 5 years: 1.2^5	2.49x
Most equity: 1,200 ÷ 2.49	482
Most you can pay: (482 + 500) ÷ 100	9.8x

One turn either side of 10x moves the IRR by about five points.

The formulas

Entry equity = EBITDA₀ × entry multiple − debt; debt = turns × EBITDA₀

Price lands on the equity.

Exit equity = EBITDAₙ × exit multiple − exit debt

The same whatever you paid.

MOIC = exit equity ÷ entry equity; IRR = MOIC^(1/n) − 1

The same exit over a bigger check is a lower return.

Target MOIC = (1 + target IRR)^n

Turn the hurdle into a multiple.

Max entry multiple = (exit equity ÷ target MOIC + debt) ÷ EBITDA₀

The most you can pay for the return you need.

Worked example

Price to equity check, plan to exit equity, then MOIC and IRR.

Drawing the numbers…

See it move

Same company at the same asking price and debt. Change the plan and the fund's hurdle, and watch what the price is worth.

Drawing the numbers…

Try this

Move any slider. The two equity checks never change, because none of these inputs touches the price or the debt. Everything happens at exit.
Raise growth. Exit equity, both IRRs and the most you can pay all rise.
Raise the hurdle. Neither IRR moves, but the most you can pay falls.
Compare the IRR bars. One turn cheaper always wins, because the same exit equity sits on a smaller check.

Run it backwards

Same company, reversed: the fund needs a set IRR. What is the highest entry multiple it can bid?

Drawing the numbers…

Turn the IRR into a multiple of money. Exit equity does not depend on the price, so dividing it by that multiple gives the most equity you can put in. Add the debt the lenders will provide for the most enterprise value, and divide by EBITDA.

This is the number a sponsor takes into an auction. Bid above it and the deal only works if the plan beats the plan.

Traps

Assuming more debt comes with a higher price.

Lenders size off EBITDA. A higher price is all equity.

Lowering the exit multiple when the entry price rises.

The plan's exit does not depend on what you paid. Hold it fixed and only the check changes.

Saying a higher price means more interest.

The debt, and so the interest, is the same. The damage is entirely to the equity return.

Using the target IRR directly in the price formula.

Convert it to a multiple first: (1 + IRR)^n. Exit equity ÷ that multiple is the equity you can afford.

Planning to grow out of an expensive entry.

Growth helps at any price. Paying up means the same growth earns less, which is why the price is the lever sponsors fight hardest over.

Say it in the interview

The interviewer asks

“Why does the entry multiple matter so much in an LBO?”

Say yours out loud first, then compare.

Check yourself

4 fresh questions, with new numbers. Answer each one correctly to finish the chapter. Get one wrong and you will see the full working, then you can try it again with new numbers.

Answers within 1% are marked right. Type the number; $, %, x and M are fine. First tries count toward Learned: the topic is Learned once every chapter is done and 75% of first tries were right.

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Drawing your questions…

Remember

Debt is sized off EBITDA, so price only moves the equity.
Same exit ÷ bigger check = lower MOIC and IRR.
Max multiple = (exit equity ÷ target MOIC + debt) ÷ EBITDA.
Paying one turn more costs more IRR the higher the leverage.